Acronym ...
Name q x8o,
variation of octagonal prism
Circumradius sqrt[(3+sqrt(2))/2] = 1.485633
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between q x and q x (at q):   135°
  • between q x and x8o:   90°
Confer
uniform variant:
op  
variations:
w x8o  

using edge sizes x = 1 and q = sqrt(2) = 1.414214


Incidence matrix according to Dynkin symbol

q x8o

. . . | 16 | 1  2 | 2 1
------+----+------+----
q . . |  2 | 8  * | 2 0
. x . |  2 | * 16 | 1 1
------+----+------+----
q x . |  4 | 2  2 | 8 *
. x8o |  8 | 0  8 | * 2

q x4x

. . . | 16 | 1 1 1 | 1 1 1
------+----+-------+------
q . . |  2 | 8 * * | 1 1 0
. x . |  2 | * 8 * | 1 0 1
. . x |  2 | * * 8 | 0 1 1
------+----+-------+------
q x . |  4 | 2 2 0 | 4 * *
q . x |  4 | 2 0 2 | * 4 *
. x4x |  8 | 0 4 4 | * * 2

xx8oo&#q   → height = sqrt(2) = 1.414214
({8} || {8})

o.8o.    | 8 * | 2 1 0 | 1 2 0
.o8.o    | * 8 | 0 1 2 | 0 2 1
---------+-----+-------+------
x. ..    | 2 0 | 8 * * | 1 1 0
oo8oo&#q | 1 1 | * 8 * | 0 2 0
.x ..    | 0 2 | * * 8 | 0 1 1
---------+-----+-------+------
x.8o.    | 8 0 | 8 0 0 | 1 * *
xx ..&#q | 2 2 | 1 2 1 | * 8 *
.x8.o    | 0 8 | 0 0 8 | * * 1

xx4xx&#q   → height = sqrt(2) = 1.414214
({8} || {8})

o.4o.    | 8 * | 1 1 1 0 0 | 1 1 1 0
.o4.o    | * 8 | 0 0 1 1 1 | 0 1 1 1
---------+-----+-----------+--------
x. ..    | 2 0 | 4 * * * * | 1 1 0 0
.. x.    | 2 0 | * 4 * * * | 1 0 1 0
oo4oo&#q | 1 1 | * * 8 * * | 0 1 1 0
.x ..    | 0 2 | * * * 4 * | 0 1 0 1
.. .x    | 0 2 | * * * * 4 | 0 0 1 1
---------+-----+-----------+--------
x.4x.    | 8 0 | 4 4 0 0 0 | 1 * * *
xx ..&#q | 2 2 | 1 0 2 1 0 | * 4 * *
.. xx&#q | 2 2 | 0 1 2 0 1 | * * 4 *
.x4.x    | 0 8 | 0 0 0 4 4 | * * * 1

© 2004-2019
top of page